Development of a new form for the alpha function of the Redlich–Kwong cubic equation of state

The dependence on temperature and acentric factor of the attractive term of the Redlich–Kwong equation of state has been modified. A new alpha function is expressed in a generalized form. The new equation allows a good representation of vapor pressure data of a great variety of compounds, as well as thermodynamic properties such as the enthalpy of vaporization and the entropy of vaporization.     

A saturated liquid density equation in conjunction with the Predictive-Soave–Redlich–Kwong equation of state for pure refrigerants and LNG multicomponent systems

An equation and a set of mixing rules for the prediction of liquid density of pure refrigerants and liquified natural gas (LNG) multicomponent systems have been developed. This equation uses the parameters of Mathias and Copeman [P.M. Mathias, T.W. Copeman, Fluid Phase Equilib. 13 (1983) 91–108] temperature dependent-term for the Predictive-Soave–Redlich–Kwong [T. Holderbaum, J. Gmehling, Fluid Phase Equilib. 70 (1991) 251–265] equation of state and hence it could be used together with this equation. The equation uses a characteristic parameter for each refrigerant; however, if it is not available, a value of zero is recommended. This model gives an average of absolute errors less than 0.42% for the prediction of liquid density of 28 pure refrigerants consisting of 2489 data points and 0.33% for 18 multicomponent LNG systems involving 132 data points. The model parameters were determined from pure component properties and reported. These parameters were then used without any adjustment to predict liquid density of multicomponent LNG mixtures and excellent results were obtained. The model was also compared with other available methods.     

Prediction of the auto-ignition temperature of binary liquid mixtures based on the quantitative structure–property relationship approach

Journal of Thermal Analysis and Calorimetry - The auto-ignition temperature (AIT) is one of the most important parameters in flammability risk assessment and management in the chemical process....     

The Kwak–Mansoori approach to the Peng–Robinson equation for determining the thermodynamic consistency of VLE in ethanol + congener mixtures

The modified Peng–Robinson equation of state proposed by Kwak and Mansoori (PR/KM) is used in a thermodynamic consistency test of phase equilibrium data for binary ethanol + congener mixtures found in alcoholic distillation processes. Congener substances are those components in a must that are present at very low concentration, but their presence is necessary to give the distilled liquor their particular aromatic and tasting characteristics. The congener substances considered in this study are: acetic acid, ethyl acetate, furfural, methanol, 2-methyl-1-propanol, 1-pentanol, 1-propanol and methyl acetate. A flexible area test method is applied to analyse 25 isothermal P–x–y data of ethanol + congener mixtures available in the open literature. The consistency method determines the value of three integral expressions derived from the Gibbs–Duhem equation; one integral is calculated using experimental data only and the other two by using values calculated with the PR/KM model. For all cases, the method gives a clear answer about consistency or inconsistency of a set of isothermal P–x–y data.     

Phase equilibria study of Lennard–Jones mixtures by an analytical equation of state

The recently developed equation of state (EOS) for Lennard–Jones mixtures [Y. Tang, B.C.-Y. Lu, Fluid Phase Equilibria 146 (1998) 73.] is further investigated in this work for describing phase equilibria of these mixtures. The investigation covers vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), vapor–liquid–liquid equilibria (VLLE) and vapor–vapor equilibria (VVE) over a wide range of temperatures, pressures and molecular characteristic parameters. Results from the van der Waals one-fluid (VDW1) theory are included for comparison. The newly proposed theory performs very well for VLE and LLE and the performance is better than the VDW1 theory; but both theories yield only qualitative results for VVE. It is also found that one system should exhibit VLLE, which was not noticed in previous investigations. Results from two other perturbation theories are also compared in some cases.     

Prediction of vapor–liquid equilibria properties of several HFC binary refrigerant mixtures

New correlations have been developed to estimate saturated vapor pressures of eight HFC binary refrigerant mixtures, namely HFC125/134a, HFC125/143a, HFC134a/236fa, HFC134a/245fa, HFC143a/134a, HFC143a/152a, HFC32/125, and HFC32/134a. In this prediction method, the saturated vapor pressures of mixtures can be calculated by the thermoproperties of pure components, without any adjustable parameters determined by experimental data. The overall average absolute deviation of pressures is <1% compared with experimental data.     

An approach to calculate solid–liquid phase equilibrium for binary mixtures

An approach is presented to calculate solid–liquid phase equilibrium for binary mixtures, using expressions for the temperature as a function of the molar fraction. For Margules model the expression gives explicitly the temperature, while for other liquid phase activity models an iterative procedure is required to calculate the temperature. The method is very easy to apply and it can be used for mixtures that have peritectic and eutectic points, or just a eutectic point. The approach was applied to five case studies with binary mixtures of fatty acids and triglycerides. The results were in good agreement with experimental data.     

Comparison of methods for calculating thermodynamic properties of binary mixtures in the sub and super critical state: Lee–Kesler and cubic equations of state for binary mixtures containing either CO2 or H2S

The (ρ,T,p) and (vapor + liquid) equilibria for fluid mixtures containing either CO₂ or H₂S have been determined from 13 equations of state. The estimated values have been compared with published experimental results. CO₂ and H₂S were used to represent non-polar and polar fluids, respectively. The equations of state investigated were as follows: (a) the Lee–Kesler equation; (b) two equations that included new reference fluids for the Lee–Kesler method; (c) three so-called extended equations of state; and (d) seven cubic equations of state. After adjustment of the binary interaction parameters the predicted values differed from the experimental data by about 0.8% for CO₂ mixtures while for H₂S mixtures the uncertainty was about ±2.8%. Somewhat larger errors, although still lower than ±5%, were obtained for co-existing phase densities; the Lee–Kesler method provided results of the highest accuracy. The cubic equations proposed by Schmidt and Wenzel and Valderrama provide the most reliable predictions of both single and co-existing phase densities. Comparison of the predicted (vapor + liquid) equilibrium with experiment shows that each of the seven cubic equations provides results of similar accuracy and all within ±6%.     

Prediction of thermodynamic properties of some polymeric systems using an extended LJ potential-based equation of state up to high temperature–high pressure conditions

In this work, the extended Lennard-Jones potential-based equation of state (ELJ-based EoS) on which the effective near-neighbour pair interactions are LJ (12,6,3) type has been used to predict the specific volume and other thermodynamic properties of some semi-crystalline and liquid polymers and copolymers up to extremely high temperature–high pressure conditions. It seems that, at least in the dense regions, there are no upper- and lower-specific volume limitations in the applicability of the model for different polymeric systems. The parameters can be determined at any temperature for each compound using the temperature dependence of the parameters of ELJ-based EoS. The calculated parameters have been used to calculate the specific volume and other derived thermodynamic properties of different polymeric systems at any temperature and pressure. The ELJ-based EoS has been also compared with some previous studies.     

Separation of binary gas mixtures by means of sol–gel modified ceramic membranes. Prediction of membrane performance

Ceramic membranes based on an alumina support with two successive layers of alumina of decreasing pore size and a sol–gel top layer, were characterized by gas permeability experiments and used for separating binary H₂ and N₂ gas mixtures. A mathematical model based on mass balance calculations was developed to predict the composition of permeated gas as a function of the different experimental parameters. No gas diffusion assumption is made, and it allows, after a previous characterization of the membrane, to find the optimal conditions for gas separation.     

Liquid–liquid equilibria of copolymer mixtures based on an equation of state

Liquid–liquid equilibria of copolymer mixtures were studied by an equation of state (EoS) for chain-like fluids. The equation consists of a reference term for hetero-nuclear hard-sphere chain fluids developed by Hu et al. where the next-to-nearest-neighbor correlations have been taken into account; and a perturbation term from Alder et al.’s square-well attractive potential. The segment parameters, including number of segments, segment diameter and interaction energy between segments, are obtained by fitting pVT data of pure homopolymer. For the case of different species in the same copolymer, the interaction parameters for unlike segment pairs are obtained by fitting pVT data of pure copolymer. For the interaction between segment of homopolymer and different species in copolymer, the parameters are treated as adjustable by fitting liquid–liquid equilibria data. In the latter case, the difference between different species in a copolymer is simply neglected as an approximation. Therefore, in general, only one pair of adjustable interaction parameter is determined from LLE data. To model miscibility maps of copolymer mixtures having two or three kinds of species, the interaction parameters are obtained from the boundary between miscible and immiscible regions. The EoS used in this work can correlate phase behavior including coexistence curves, miscibility windows and miscibility maps.     

Investigations of the reduced Redlich–Kister excess properties of 1,4-dioxane + isobutyric acid binary mixtures at temperatures from 295.15 to 313.15 K

Excess molar volumes and refractive index, molar refraction deviations and isentropic compressibility changes in 1,4-dioxane + isobutyric acid binary mixtures (from 295.15 to 313.15) K. were calculated from experimental density, refractive index and sound velocity data presented in previous work. Here, these experimental values were used to test the applicability of the correlative reduced Redlich–Kister equation as well as their corresponding relative functions which are important to reduce the effect of temperature and, consequently, to reveal the effects of different types of interactions. The results of these observations have been interpreted in terms of structural effects of the solvents. The correlating equation recently proposed by Belda, has also been applied to the present system in order to assess the validity of this equation and to give thermodynamic limiting partial molar quantities interesting to evaluate solute–solvent interaction.     

Three–step method to determine the eutectic composition of binary and ternary mixtures

A three-step method to determine the eutectic composition of a binary or ternary mixture is introduced. The method consists in creating a temperature–composition diagram, validating the predicted eutectic composition via differential scanning calorimetry and subsequent T-History measurements. To test the three-step method, we use two novel eutectic phase change materials based on \(\mathrm{Zn}(\hbox {NO}_3)_2\cdot 6\mathrm{H}_{2}{\mathrm O}\) and \(\mathrm{NH}_4\mathrm{NO}_3\)   respectively \(\mathrm{Mn}(\hbox {NO}_3)_2\cdot 6\mathrm{H}_{2}{\hbox {O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) with equilibrium liquidus temperatures of 12.4 and 3.9  \(\,^{\circ }\mathrm {C}\) respectively with corresponding melting enthalpies of 135 J \(\mathrm{g}^{-1}\) (237 J \(\mathrm{cm}^{-3}\) ) respectively 133 J \(\mathrm{g}^{-1}\) (225 J \(\mathrm{cm}^{-3}\) ). We find eutectic compositions of 75/25 mass% for \(\mathrm{Zn}(\hbox {NO}_3)_2\cdot \mathrm{6H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) and 73/27 mass% for \(\mathrm{Mn}(\hbox {NO}_3)_2\cdot 6\mathrm{H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) . Considering a temperature range of 15 K around the phase change, a maximum storage capacity of about 172 J \(\mathrm{g}^{-1}\) (302 J \(\mathrm{cm}^{-3}\) ) respectively 162 J \(\mathrm{g}^{-1}\) (274 J \(\mathrm{cm}^{-3}\) ) was determined for \(\mathrm{Zn}(\hbox {NO}_3)_2\cdot \mathrm{6H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) respectively \(\mathrm{Mn}(\hbox {NO}_3)_2\cdot \mathrm{6H}_{2}{\mathrm{O}}\) and \(\mathrm{NH}_4\mathrm{NO}_3\) .     

Reduced Redlich–Kister functions and interaction studies of Dehpa + Petrofin binary mixtures at 298.15 K

In order to understand the effect of different types of interactions in liquid mixtures by applying the correlative reduced Redlich–Kister equation, excess molar volume, excess dielectric constant, deviation in refractive index, deviation in molar refraction and molar polarisation were calculated at the temperature 298.15 K and atmospheric pressure P = 101.325 kPa for the binary mixture Petrofin (1) + Dehpa (2). The experimentally determined data of density and refractive index which were published earlier were used for these calculations. The results were interpreted in terms of structural effects of the solvents.     

Calculating the Critical Properties of Multicomponent Mixtures Using the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) Equations of State,Based on the Binary Interaction Parameters

Russian Journal of Physical Chemistry A - A way of estimating the binary interaction parameters (below, BIPs) for the semi-empirical Soave–Redlich–Kwong (SRK) and Peng–Robinson...     

Solid–liquid phase equilibrium and mixing thermodynamic analysis of coumarin in binary solvent mixtures

The solubility of coumarin in three aqueous solvent mixtures (methanol + water, ethanol + water and acetone + water) was experimentally determined by a gravimetric method at atmospheric pressure. The experimental solubility data were fitted using the modified Apelblat equation, non-random two-liquid (NRTL) equation, the combined nearly ideal binary solvent/Redlich–Kister equation and the Jouyban?Acree equation, respectively. All the equations were proven to be able to correlate the experimental data, and the modified Apelblat equation could obtain better correlation results than the other three models. The solubility of coumarin increases with increase in temperature. At the same temperature, the solubility increases with increase in mole fraction of organic solvents except for the ethanol–water system which shows a unimodal curve. In addition, the apparent thermodynamic properties of the mixing process were calculated based on the NRTL model and the experimental solubility data.     

Interaction parameter for hydrogen-containing mixtures in the Peng—Robinson equation of state

A new correlation for the Peng—Robinson interaction parameter δ_ij of hydrogen-containing mixtures is proposed here. Values of δ_ij obtained from literature vapour—liquid equilibrium data are represented by a cubic polynomial in terms of the temperature. The correlation predicts better values than other correlations proposed in the literature for the same systems, and is applicable to wider ranges of temperature. Applications of the proposed equations to VLE are presented.